Question

The average of 13 numbers is 20.If the average of first 6numbers is 18 and that of the last 6numbers is 21 find the 7th number

Answer 1

Answer:

The 7th number is 26

Step-by-step explanation:

Average = Sum of observations / No. of observations

The average of all 13 numbers = 20

=> Sum of the 13 numbers (S) = 13*20 = 260

=> S = 260

Average of first 6 numbers = 18

=> Sum of first 6 numbers (S1) = 6*18 = 108

=> S1 = 108

Average of last 6 numbers = 21

=> Sum of last 6 numbers (S2) = 6*21 = 126

=> S2 = 126

Let "x" be the unknown 7th number.

Clearly,

S = S1 + x + S2

260 = 108 + x + 126

260 = 234 + x

x = 260 - 234

x = 26

Check:

The sum of all 13 numbers = 108 + 26 + 126 = 260

Average of 13 numbers = 126/13 = 20

Answer 2

Answer:

18

Step-by-step explanation:

let the first six numbers be a, b, c, d , e, f

therefore

a+b+ c+ d + e + f/6=18

or, a+b+ c+ d + e + f=108

And,

let the last six numbers be h,i,k,l,m,n

we know,

h+i+k+l+m+n/6= 21

or, h+i+k+l+m+n=126

therefore

let g be the 7 th no.

and g= 126-108= 18